Please, go try to play one of the DDs you speak of and ONLY use your GUNS and fight a bb. The match will end before you are able to get them down to half health. Assuming you dont sink and or lose all your turrets.

Like whats previously been said, repair cost #1 reason. IMO
However,
When BB stay far back and snipe cruisers cant push or they will be slaughtered and also cruiser AA needs to protect the BB from CV's.
And when DD are spamming spreads of torpedo's people will refuse to want to move any closer. This is especially understandable when there are no CV's in the match spotting torps and DD. And MM loves to place 3-4 shimakaze's on one team and give the other team 1 shimakaze and a fubuki because balance rite m8?

Seems like everyone think its fine, but I agree with OP. Almost EVERY single game I've been having its either one team has 5-6 IJN dds, vs 2-3 US/VMF dd. And let me tell you.... The US and VMF dd cant be the dd killing gunboats they are when they are spotted the entire match.
There needs to be a DD limit of 3-4.
6 is way to much especially in Higher tiers where you have 2-3 shimakaze's+ 1-2 Kagero's and 1-2 Fubuki's. Funny those are all IJN dds.... as a exclusive dd and cruiser player I cant imagine playing BBs in high tiers!

Yeah I know making us redo all our skill points for FREE. I mean I REALLY REALLY wanted to spend 60000 doubloons so I could reset my captains but they let me do it for free? Whats wrong with wargaming and their updates!

So a new 4 point captain skill has been added that adds 400 health plus every tier to your ship.
If you were to get this skill does the repair cost of the ship change at all by increasing the health point pool?

Not to mention the US dds will almost always win in a 1v1 against RU dd in close range due to the fact is can fire almost twice as fast and its shell arc is just fine under 7-8 km.
And it will also always have the detection advantage, being able to get the first shots off and ambush. And of course taking out 1-2 turrets before RU dd even knows whats going on.
Im hoping the Udaloi and khabarovsk will be able to 1v1 US dds in t9 and t10.

I actually think its worse harassing a bb at long range in a US DD. RU DD are the fastest ships in the game, 90 percent of the time I don't even have to turn, I just sail straight at 12+ km and bbs just cant hit me, even if they get perfect lead they will often miss because of dispersion anyways. Plus AP on the RU dds is insane, you can land constant 2-3k hits on a bb at your max range..., i've citadeled cruisers at 10km, and the closer... the better you cant citadel anything in a us dd at that range for sure. Unless a cruiser gives broadside at like 3 km where your arc is flat enough you might, but even then...
If you want to use torps play US, if you dont care as much about using torps then play RU dd, and use the torps like secondaries.
Keep in mind RU torps are lightning fast and you carry plenty to nuke a bb you can setup an ambush on!

I've racked up a decent amount of battles in my Gnevny, and the Anshan seems very similar (But better). So I dont own it, but what I can say if it is anything like the Gnevny it will be very good. Even in T6. The turret traverse isnt much of a problem if you stay farther back, I mean the advantage of the 130mm guns is fast velocity, low arc. So if you stay farther back and not duel other dds at close range you will always come out on top. And the 130mm's are hilarious vs. cruisers you will be able to rack up a lot of citadels who think they can sail broadside on.
Overall just looking at it and comparing it to the grem and gnevny seems like a pretty decent DD, so if you've played those ships and liked them I think you would like it but its your decision and money.
One last thing to consider is, are you looking for something to have fun in and sink stuff? Credits? Or to train other captains (Which the Anshan can't do).

Yeah Nurnberg and most of the German line are "Glass Cannons" speeking of Nurnberg, I landed 5 Cits at 12km on one yesterday in my ARP Myoko... Good times... Goooood timmmeeeesss...
Stay back at range, always angle its a pretty cool ship. Id say its better than the yorck at least....